Euler method

[′oi·lər ‚meth·əd]

(mathematics)

A method of obtaining an approximate solution of an ordinary differential equation of the form dy / dx = f (x, y), where f is a specified function of x and y. Also known as Eulerian description.

(mechanics)

A method of studying fluid motion and the mechanics of deformable bodies in which one considers volume elements at fixed locations in space, across which material flows; the Euler method is in contrast to the Lagrangian method.

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References in periodicals archive

If we apply the half-explicit Euler method which was proposed in [17] to the test DAE (3.16), then we obtain the DAE stability function

RUNGE-KUTTA METHODS REVISITED FOR A CLASS OF STRUCTURED STRANGENESS-FREE DIFFERENTIAL-ALGEBRAIC EQUATIONS

To estimate the depth of the deep structures, the Euler method is applied the RTE-TMI map.

Mapping of Deep Tectonic Structures of Central and Southern Cameroon by an Interpretation of Surface and Satellite Magnetic Data

[11,12] studied the Vaserstein bound for Euler method and they proved an O([h.sup.(2/3-epsilon])]) for a one-dimensional diffusion process where h is the step-size and then they generalize the result to SDEs of any dimension with 0(h[square root of log(1/h))] bound when the coefficients are time-homogeneous.

The Implementation of Milstein Scheme in Two-Dimensional SDEs Using the Fourier Method

As we all know, there are many solutions corresponding to the second-order ODEs, including the Euler method, the improved Euler method and the Runge-Kutta method et al.

The Improved Velocity-based Models for Pedestrian Dynamics

The results provided by the presented method will be compared with those by the modified Euler method, Newmark method, widely-used fourth-order RK method, and the exact results, respectively.

A Highly Accurate Approach for Aeroelastic System with Hysteresis Nonlinearity

The direct application of the method to such pathological cases has been compared with the classical Euler method, showing that singularity and ambiguity drawbacks do not affect the proposed solution.

Multitemporal Volume Registration for the Analysis of Rheumatoid Arthritis Evolution in the Wrist

The numerical properties of impulsive differential equations attracted attentions of scholars since Ran et al.'s work in [7], which showed that the explicit Euler method is stable for impulsive differential equations, while the implicit Euler method is not.

Stability Analysis of Analytical and Numerical Solutions to Nonlinear Delay Differential Equations with Variable Impulses

Here [theta] = 0 defines the explicit Euler method, [theta] = 1 defines the backward Euler method and [theta] =1/2 gives the symmetric (or trapezoidal) Euler method [13].

On Stability Analysis of Finite Difference Schemes for Generalized Kuramoto-Tsuzuki Equation with Nonlocal Boundary Conditions